So you mean what you said an "inverter" not an UPS. I think you use the inverter in power failure situation and it shuts off the PC within few minutes, so the reason could be the inverter was not supplying enough power to run the PC for longer period of time. It also depends on how power hungry is your system. It has nothing to do with your GPU. And frankly I don't understand your real situation. Please post in details and with your full system specs.